For the definition and a thorough treatment of Hausdorff dimension we refer
to the book by Falconer [1]}.
To obtain a lower bound for the Hausdorff dimension we will use the following
result known as the mass distribution principle [1]}.
Here and in the following we use the notation \(B(x,r)\)  for the open ball of
radius \(r\)  around a point \(x\in \mathbb {R}^d\) . Sometimes we will emphasize the dimension
by writing \(B_d(x,r)\)  instead of \(B(x,r)\) .
The closed ball is denoted by \(\overline{B}(x,r)\) .
